The main objective of this study is to estimate the hydrodynamic forces and to investigate the nonlinear behaviors of fluid motion around the oscillating body on or below a free surface. We have developed a composite grid method to solve the radiation problems. This method is applied to numerical computation of the radiation forces generated by the oscillating body. The numerical results obtained by the present method are compared with the experimental data and a linear potential theory. As a result, we can confirm the accuracy of the present method. Finally, we have evaluated the effect of viscosity on the hydrodynamic forces acting on the oscillating body.